Compare Rational Numbers

A rational number is any number that can be expressed as a fraction \( \frac{p}{q} \) where:

• \( p \) is an integer.
• \( q \) is an integer, but \( q \) cannot be zero.

Check out the following lesson if you need to review what is a rational number:
Rational Numbers

How to compare rational numbers?
Comparing rational numbers involves determining which of two or more rational numbers is greater than, less than, or equal to the others. Since rational numbers can be expressed as integers, fractions or decimals, we can use various methods to compare them. Here are some of the methods:

Convert to Decimals Method
a) Divide the numerator by the denominator for each fraction to get its decimal representation.
b) Once all numbers are in decimal form, compare them as you would compare any decimal numbers, by looking at the digits from left to right.

This method is useful if you need to compare many rational numbers or if the rational numbers are expressed in different forms: fractions, integers, and decimals. You can convert all the fractions to decimals and then compare.

The following diagram gives some examples of comparing and ordering rational numbers. Scroll down the page for more examples and solutions.

 

Refer to the following lesson if you need to review how to compare integers and decimals:
Compare and Order Integers
Compare and Order Decimals

Fraction, Decimal & Rational Number Worksheets
Practice your skills with the following worksheets:
Online & Printable Fraction Worksheets
Online & Printable Decimal Worksheets
Online & Printable Rational Number Worksheets

Cross-Multiplying Method (for comparing two fractions)
If you have two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \) (where \( b \) > 0 and \( d \) > 0), you can compare them by cross-multiplying:

• if \( ad \) > \( bc \) then \( \frac{a}{b} \) > \( \frac{c}{d} \)
• if \( ad \) < \( bc \) then \( \frac{a}{b} \) < \( \frac{c}{d} \)
• if \( ad \) = \( bc \) then \( \frac{a}{b} \) = \( \frac{c}{d} \)

Common Denominator Method

1. For fractions, find the least common multiple (LCM) of the denominators.
2. Convert each fraction to an equivalent fraction with this common denominator.
3. Once the denominators are the same, compare the numerators. The fraction with the larger numerator is the larger fraction.

Number Line Method
Place the rational numbers on a number line by relating them to common benchmarks like -1, -1/2, 0, 1/2, 1

General Rules for Comparing Rational Numbers:

• Positive vs. Negative: Any positive rational number is greater than any negative rational number.
• Negative vs. Zero: Zero is greater than any negative rational number.
• Positive vs. Zero: Any positive rational number is greater than zero.
• Negative vs. Negative: Compare their absolute values (the larger absolute value is smaller).

Comparing and Ordering Rational Numbers
This video describes three methods of comparing rational numbers to each other (“greater than” or “less than”), and how to order rational numbers from least-to-greatest or greatest-to-least.

• Show Step-by-step Solutions

How to Compare and Order Rational Numbers?

• Show Step-by-step Solutions

How to compare rational numbers using a number line?
Example:
Look at the rational numbers below. Order them from least to greatest.
1/2, -5, 3.3, 0, 21/12, -5.5, 2 1/8

• Show Step-by-step Solutions

Comparing and ordering rational numbers
Example:
4 1/5, -3.6, -3 8/9, 0

• Show Step-by-step Solutions

Comparing and ordering rational numbers by converting to decimals
Examples:
3/8, 4/9, 7/12, 7/15
0.6. 0.84, 87/100, 1 7/9, 11/6, 2.5

• Show Step-by-step Solutions

Ordering three rational numbers (decimal, percent, fraction) from least to greatest
Example:
Order the following number from least to greatest
0.7, 7%, 3/4

• Show Step-by-step Solutions

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.